Engineering Board Exam Reviewer · Exact Differential Equations · medium

Determine whether (y x+2xey),dx+( x+x2ey),dy=0 is exact.

  1. Yes, it is exact
  2. No, it is not exact
  3. Only exact when y=0
  4. Cannot be determined without solving

Answer

A. Yes, it is exact

Solution

With M=y x+2xey and N= x+x2ey: M/ y= x+2xey and N/ x= x+2xey. Since these are equal, the equation is exact.

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